MHT CET · Physics · Nuclear Physics
A nucleus breaks into two nuclear parts, which have their velocity ratio \(2: 1\). The ratio of their nuclear radii will be
- A \(\sqrt{2}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{2^{1 / 3}}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2^{1 / 3}}\)
Step-by-step Solution
Detailed explanation
By law of conservation of momentum, the two parts will have equal and opposite momentum, assuming the nucleus was initially at rest.
\(
\begin{aligned}
& \therefore \mathrm{m}_1 \mathrm{v}_1=\mathrm{m}_2 \mathrm{v}_2 \text { or } \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{\mathrm{v}_2}{\mathrm{v}_1}=\frac{1}{2} \\
& \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{1}{2} \\
& \therefore \frac{\mathrm{r}_1}{\mathrm{r}_2}=\frac{1}{2^{1 / 3}}
\end{aligned}
\)
\(
\begin{aligned}
& \therefore \mathrm{m}_1 \mathrm{v}_1=\mathrm{m}_2 \mathrm{v}_2 \text { or } \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{\mathrm{v}_2}{\mathrm{v}_1}=\frac{1}{2} \\
& \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{1}{2} \\
& \therefore \frac{\mathrm{r}_1}{\mathrm{r}_2}=\frac{1}{2^{1 / 3}}
\end{aligned}
\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A mass ' \(M\) ' is suspended from a light spring. An additional mass \(\mathrm{M}_1\) added extends the spring further by a distance ' \(\mathrm{x}\) '. Now the combined mass will oscillate on the spring with period \(\mathrm{T}=\)MHT CET 2023 Hard
- A disc of radius 0.4 meter and mass \(1 \mathrm{~kg}\) rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration is \(10 \mathrm{rad} \mathrm{s}^{-2}\). The tangential force applied to the rim of the disc isMHT CET 2021 Hard
- The ratio of energy required to raise a satellite to a height ' \(h\) ' above the earth's surface to that required to put it into the orbit at the same height is ( \(\mathrm{R}=\) radius of earth)MHT CET 2023 Medium
- A plane wavefront is incident on a water surface at an angle of incidence \(60^{\circ}\) then it gets refracted at \(45^{\circ} .\) The ratio of width of incident wavefront to that of refracted
wavefront will be \(\left[\sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}, \sin 60^{\circ}=\frac{\sqrt{3}}{2}, \cos 60^{\circ}=\frac{1}{2}\right]\)MHT CET 2020 Medium - The ratio of the wavelength of the last line of Paschen series to that of Balmer series isMHT CET 2025 Medium
- The resultant gate and its Boolean expression in the given circuit is
MHT CET 2021 Medium
More PYQs from MHT CET
- If two dice are thrown together. Then, the probability that the sum of the numbers appearing on them is a prime number, isMHT CET 2010 Medium
- Which among following statement is NOT true for neoprene?MHT CET 2021 Easy
- Select the CORRECT statements:
i. Tubular secretion involves secretion of \(H ^{+}\)ions in PCT.
ii. Augmentation involves secretion of \(H ^{+}\)ions in DCT and CT.
iii. Augmentation plays an important role in regulation of pH of blood.
iv. Glomerular filtrate as well as urine are acidic. Select the correct option:MHT CET 2024 Easy - If \(x=\sec \theta, y=\tan \theta\), then the value of \(\frac{d^{2} y}{d x^{2}}\) at
\(\theta=\frac{\pi}{4}\) isMHT CET 2010 Easy - What is bond order of \(\mathrm{F}_2\) molecule?MHT CET 2023 Easy
- If \(\int \frac{\log \left(t+\sqrt{1+\mathrm{t}^2}\right)}{\sqrt{1+\mathrm{t}^2}} \mathrm{dt}=\frac{1}{2}(\mathrm{~g}(\mathrm{t}))^2+\mathrm{c}\)
where c is a constant of integration, then \(g(2)\) is equal toMHT CET 2024 Hard